This book gives the definitive mathematical answer to what thermodynamics really is: a
variational calculus applied to probability distributions. Extending Gibbs's notion of ensemble
the Author imagines the ensemble of all possible probability distributions and assigns
probabilities to them by selection rules that are fairly general. The calculus of the most
probable distribution in the ensemble produces the entire network of mathematical relationships
we recognize as thermodynamics.The first part of the book develops the theory for discrete and
continuous distributions while the second part applies this thermodynamic calculus to problems
in population balance theory and shows how the emergence of a giant component in aggregation
and the shattering transition in fragmentation may be treated as formal phase transitions.While
the book is intended as a research monograph the material is self-contained and the style
sufficiently tutorial to be accessible for self-paced study by an advanced graduate student in
such fields as physics chemistry and engineering.
